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Magic squares, their origins lost in antiquity, are among the more popular mathematical recreations. "Magic" ideas have also been applied to graphs, labellings, and trees. Unlike many elusive subjects in this area, the problem for vertex-magic total labelings has been solved, and the details are examined in this volume.
Contents Preface * List of Figures * 1. Preliminaries * 1.1 Magic * 1.2 Graphs * 1.3 Labelings * 1.4 Magic Labeling * 1.5 Some Applications of Magic Labelings * 2. Edge-Magic Total Labelings * 2.1 Basic Ideas * 2.2 Graphs with No Edge-Magic Total Labelings * 2.3 Cliques and Complete Graphs * 2.4 Cycles * 2.5 Complete Bipartite Graphs * 2.6 Wheels * 2.7 Trees * 2.8 Disconnected Graphs * 2.9 Strong Edge-Magic Total Labelings * 2.10 Edge-Magic Injections * 3. Vertex-Magic Total Labelings * 3.1 Basic Ideas * 3.2 Regular Graphs * 3.3 Cycles and Paths * 3.4 Vertex-Magic Total Labelings of Wheels * 3.5 Vertex-Magic Total Labelings of Complete Bipartite Graphs * 3.6 Graphs with Vertices of Degree One * 3.7 The Complete Graphs * 3.8 Disconnected Graphs * 3.9 Vertex-Magic Injections * 4. Totally Magic Labelings * 4.1 Basic Ideas * 4.2 Isolates and Stars * 4.3 Forbidden Configurations * 4.4 Unions of Triangles * 4.5 Small Graphs * 4.6 Totally Magic Injections * Notes on the Research Problems * Bibliography * Solutions to Selected Exercises * Index
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